Surface tension effects were recognized centuries ago and recorded by Leonardo da Vinci (1452-1519) who observed the rise of a fluid in a small tube, which was subsequently termed "capillarity." The forces of adhesion and cohesion in fluids were later recognized by Sir Isaac Newton (1642-1727). The maximum bubble pressure method of measuring surface tension was first suggested by Simon in 1851 and later developed by Jaeger in 1917. The theory had earlier been developed by Cantor in 1892. Sugden, in 1921, developed apparatus that utilized the technique to measure surface tension in fluids in a laboratory setting.
Present laboratory methods for making intermittent (single fluid sample) surface tension measurements include the Wilhelmy Plate method, Du Nouy ring, sessile drop, pendant drop, capillary height, drop weight, and maximum bubble pressure.
No continuous process instrument for measuring surface tension is presently being marketed; only laboratory units using techniques mentioned earlier.
U.S. Pat. No. 3,426,584 suggests a double tube bubble pressure method with two orifices submerged into the liquid at the same depth, with accuracies claimed to be "about two percent."
An instrument using two unequal sized orifice tubes immersed in a process fluid at the same horizontal depth through which process gas is bubbled had been suggested for use in a chemical engineering laboratory environment using a flow-through vessel in which a process liquid is introduced in a continuous stream and into which gas bubbles are introduced under the fluid surface using two fixed orifices of different diameters. This arrangement required precise manual valve adjustments to produce bubbling of gas through the orifices and fluid flow through the cell at the desired rate. Accuracy of this device is claimed to be in the 1-2% range.
There is a need for an on-line surface tension measurement device with in-process accuracies of one percent or less with 1/2 dyne precision--levels never previously achieved by any prior art techniques--but there is not presently available to industry any such a device, for use in an ongoing process environment, especially where the pressure within the vessel holding the liquid or the liquid level may vary while the surface tension measurements are being made.
In order to measure surface tension accurately in an in-process, on-line environment, it is necessary that the method chosen be as immune as possible to external environmental and other potential contaminating effects. For example, there is sufficient grease from one's finger to lower the surface tension of water from 72 dynes/cm to well below 65 dynes/cm after touching a clean water surface when measurements are made using a surface film measurement technique.
The maximum bubble pressure method, or a variation thereof, can avoid such error-causing effects by measuring surface tension within the body of the test fluid if accurate pressure measurements related to surface tension, due to the gas bubble--fluid interface, can be made. No method to date, however, had completely resolved the physical problems associated with blowing a bubble of gas inside a fluid body and measuring the maximum bubble pressure of this bubble with sufficient accuracy so that all of the effects influencing the pressure value, such as liquid density, radius of the bubble tube orifice, gravitational constant and depth of bubble formation are fully and accurately identified, measured, and resolved.
The basic equation describing surface tension can be written as follows, and is a multiple term, non-linear equation, referred to hereafter as the modified Schroedinger equation: ##EQU1## Where: .gamma. is the surface tension
.rho. is the density of the liquid PA1 P.sub.1 is the maximum pressure of bubble at small orifice PA1 P.sub.2 is the maximum pressure of bubble at large orifice PA1 r.sub.1 is the radius of the small orifice PA1 r.sub.2 is the radius of the large orifice PA1 (h.sub.1 -h.sub.2) is the difference in depth of the orifices PA1 g is the gravitational constant
As can be seen by the above modified Schroedinger equation, an apparatus that measures surface tension directly must resolve the non-linear multiple terms in this equation. If the orifices are at the exact same height, the second term in the above equation is eliminated.
Orifices must be designed in such a manner that the bubbles produced are ones of constant and consistent size. If a fluid has good wetting properties the end of the capillary tube will be wetted so that the radius of the formed bubble will be the internal tube radius of the orifice. As the liquid recedes to the outer edge, with decreased wetting properties, the bubble radius will approach the outside tube radius of the orifice. This effect was recognized in the surface tension measurement apparatus described in U.S. Pat. No. 2,401,053.
Orifices of previously designed apparatus were designed incorporating fixed tube orifice ratios, either as part of the beaker assembly, or as part of the entire apparatus assembly. The Smith U.S. Pat. No. 3,426,584 fixed the ratio and limited the size of the orifices (r.sub.1 &lt;0.01 cm, r.sub.2 &lt;0.2 cm) in an attempt to negate the second and third terms of the equation used in his patent. This does not recognize that ideally the small orifice must be as small as possible because as the bubble gets smaller, it becomes more spherical and the back pressure due to surface tension effects approaches the value 2 .gamma./r, where r is the radius of the orifice.
A single small orifice pressure equation can be written as P=.rho.gh+2.gamma./r, and therefore, if the larger of the two orifices can be used to measure the head (h) effect the smaller orifice will approach more accurately the true surface tension value, 2 .gamma./r. The limitation in practice comes about by physical orifice configurations, fluids that may tend to coagulate and plug orifices, and pneumatic control system configurations.
If the ratios of the two orifices are small (as the sizes decrease in difference) the signals generated become closer in magnitude requiring more electronic filtering and more costly and complicated electronics.
Different orifice sizes will result in different magnitudes of error for the constant term (third term) and non-linear term (fourth term) in the surface tension equation. By using very large and very small orifice sizes, the error terms can be reduced substantially. The error, even if reduced, however, must still be considered if accurate surface tension values are desired. Conversely, if one orifice cannot be very large and the other very small because of physical or fluid considerations mentioned earlier, the error term calculation must correct for inaccurate apparatus output values either manually using a correction chart, or electronically.
Fixed orifices that are fixed as part of the fluid containment vessel lack flexibility because cleaning is more difficult when process fluids change, or different intermittent measurements are required.
Pneumatic control of the bubble rate of the process gas is important for accuracy of surface tension readings. As the level of fluid changes (changing head), increased back pressure will slow down or stop the bubble rate. This precludes the use of existing prior art measurement systems under conditions where varying head or varying pressure conditions exist, such as in pressurized in-process or in-reactor applications. Regulating equipment that will regulate pressure accurately can allow higher pressure or higher head conditions but still will not work well under pressure fluctuation systems. Regulators will compensate for incoming process gas fluctuations but not downstream fluctuations at the orifice.
Proximity of the orifices to one another must be considered since some vibration resonance occurs as bubbles break off at the orifice and rise to the fluid surface. This causes acoustic coupling effects that can add error signals at the sensing transducer. Additionally, the orifices cannot be located too close to the side of the fluid containment vessel so as to impede the free forming and free release of the gas bubble. Motion of the fluid, as in a flow-through vessel, must be such that it does not shear the bubbles from the orifice tips as they form and thereby reduce the desired spherical bubble shape.
Bubbles at the orifice must be formed in a controlled manner. When a fluid-gas surface is formed, a finite time is required to establish equilibrium in the surface phase, and during this period the surface tension is time dependent. The bubble frequency must, therefore, be kept low enough to allow discrete independent bubbles to form.
The pressure signals formed at the small and large orifices take the approximate form of saw-tooth waves. While a differential pressure transducer will subtract the output signals, the net result will still be in the form of a saw-tooth output of very low frequency. Attention must, therefore, be given to the response of any filter circuit that is used to time-average the differential output signal. Cutoff frequency must be low enough to filter out transients and harmonics while time delay must compromise between response and stability.
As the surface area of a pure liquid is increased adiabatically and work is performed on the liquid system, the temperature will drop and the surface tension will increase to constrain expansion. This effect explains the relationship between surface tension and temperature and why, therefore, the surface tension of pure liquids will generally increase as the temperature decreases and vice versa. It is, therefore, necessary to recognize and deal with the surface tension-temperature relationship when surface tension measurements are made.
Existing measurement methods, such as the Du Nouy ring, capillary height and others previously mentioned, require a clear surface without surface contaminants in order to obtain accurate surface tension measurements. These methods, therefore, cannot be used in instances where surface foaming occurs or surface debris is present. These methods will measure surface tension at the topmost level of the test vessel fluid and cannot indicate whether the fluid itself is homogeneous or the reading is due only to a thin surface film, which may have different properties than the bulk of the fluid.